Entanglement Entropy Scaling Law in the Ground State of Supersymmetric Fermion Lattice Model

We investigate the entanglement entropy in the ground state of the supersymmetric fermion lattice
model. The Hamiltonian of this model is block diagonal in the basis of a fixed number of particles, so we compute the entanglement entropy for the blocks of the Hamiltonian separately. We explain the way of calculating
the correlation matrix and the entanglement entropy for the ground state of supersymmetric Hamiltonian on
diverse graphs. Then we show that the entanglement entropy exhibits the volume law scaling in various
choices of the number of fermions in regular graphs. Also, we give the analytical formula for the entanglement
entropy in one scalable set of strongly regular graphs in terms of their parameters, and we prove that the
entanglement entropy satisfies a volume law.